InertiaMoment2d

Measures the resistance of an object, defined by a two-dimensional binary image, to changes in its motion around a given axis of rotation.

Access to parameter description

For an introduction:

section Image Analysis
section Moment And Orientation

This algorithm computes a measurement of an object's resistance to changes in its rotational motion.
The moment of inertia of an object on a given axis describes how difficult it is to change its angular motion around this axis.

For a point mass

$m$ , the moment of inertia

$I$ is simply

$m$ times the square perpendicular distance

$r$ from the axis of rotation:

$I = mr^2$ On a digital image, a pixel intensity can be considered as a mass.
Then, for an object of a binary image,

$m$ is a constant equal to 1. Thus, the moment of inertia is the sum of the square perpendicular distances from the axis:

$I = \sum_r r^2 = \sum_x(x-p(x))^2$ where:

$x$ is an object pixel
$p(x)$ is the orthogonal projection of $x$ onto the axis of rotation.

The rotation axis is defined by a point (rotationCenterX and rotationCenterY) and an orientation (rotationAngle), which are user-defined parameters.

See also

Function Syntax

This function returns the outputMeasurement output parameter.

// Function prototype.
MeanInertiaMomentMsr::Ptr
inertiaMoment2d( std::shared_ptr< iolink::ImageView > inputBinaryImage,
                 int32_t rotationCenterX,
                 int32_t rotationCenterY,
                 double rotationAngle,
                 MeanInertiaMomentMsr::Ptr outputMeasurement = NULL );

This function returns the outputMeasurement output parameter.

// Function prototype.
inertia_moment_2d( input_binary_image,
                   rotation_center_x = 1024,
                   rotation_center_y = 1024,
                   rotation_angle = 10,
                   output_measurement = None )

This function returns the outputMeasurement output parameter.

// Function prototype.
public static MeanInertiaMomentMsr
InertiaMoment2d( IOLink.ImageView inputBinaryImage,
                 Int32 rotationCenterX = 1024,
                 Int32 rotationCenterY = 1024,
                 double rotationAngle = 10,
                 MeanInertiaMomentMsr outputMeasurement = null );

Class Syntax

// Command constructor.
InertiaMoment2d();

// Get method of the inputBinaryImage parameter.
std::shared_ptr< iolink::ImageView > inputBinaryImage() const;
// Set method of the inputBinaryImage parameter.
void setInputBinaryImage( std::shared_ptr< iolink::ImageView > inputBinaryImage );

// Get method of the rotationCenterX parameter.
int32_t rotationCenterX() const;
// Set method of the rotationCenterX parameter.
void setRotationCenterX( const int32_t& rotationCenterX );

// Get method of the rotationCenterY parameter.
int32_t rotationCenterY() const;
// Set method of the rotationCenterY parameter.
void setRotationCenterY( const int32_t& rotationCenterY );

// Get method of the rotationAngle parameter.
double rotationAngle() const;
// Set method of the rotationAngle parameter.
void setRotationAngle( const double& rotationAngle );

// Get method of the outputMeasurement parameter.
MeanInertiaMomentMsr::Ptr outputMeasurement() const;

// Method to launch the command.
void execute();

// Property of the inputBinaryImage parameter.
InertiaMoment2d.input_binary_image
// Property of the rotationCenterX parameter.
InertiaMoment2d.rotation_center_x
// Property of the rotationCenterY parameter.
InertiaMoment2d.rotation_center_y
// Property of the rotationAngle parameter.
InertiaMoment2d.rotation_angle
// Property of the outputMeasurement parameter.
InertiaMoment2d.output_measurement

// Method to launch the command.
execute()

// Command constructor.
InertiaMoment2d()

// Property of the inputBinaryImage parameter.
InertiaMoment2d.inputBinaryImage
// Property of the rotationCenterX parameter.
InertiaMoment2d.rotationCenterX
// Property of the rotationCenterY parameter.
InertiaMoment2d.rotationCenterY
// Property of the rotationAngle parameter.
InertiaMoment2d.rotationAngle
// Property of the outputMeasurement parameter.
InertiaMoment2d.outputMeasurement

// Method to launch the command.
Execute()

Parameters

Class Name	InertiaMoment2d

	Description	Type	Supported Values	Default Value
inputBinaryImage	The input binary image.	Image	Binary	nullptr
rotationCenterX	The X pixel coordinate of the rotation axis.	Int32	>=1	1024
rotationCenterY	The Y pixel coordinate of the rotation axis.	Int32	>=1	1024
rotationAngle	The orientation of the rotation axis in degrees. A positive value means that the angle is taken from the positive X axis to the positive Y axis.	Float64	Any value	10
outputMeasurement	The output measurement result.	MeanInertiaMomentMsr		nullptr

Object Examples

auto polystyrene_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene_sep.vip" );

InertiaMoment2d inertiaMoment2dAlgo;
inertiaMoment2dAlgo.setInputBinaryImage( polystyrene_sep );
inertiaMoment2dAlgo.setRotationCenterX( 1024 );
inertiaMoment2dAlgo.setRotationCenterY( 1024 );
inertiaMoment2dAlgo.setRotationAngle( 10 );
inertiaMoment2dAlgo.execute();

std::cout << "meanMoment: " << inertiaMoment2dAlgo.outputMeasurement()->meanMoment( 0 ) ;

polystyrene_sep = imagedev.read_vip_image(imagedev_data.get_image_path("polystyrene_sep.vip"))

inertia_moment_2d_algo = imagedev.InertiaMoment2d()
inertia_moment_2d_algo.input_binary_image = polystyrene_sep
inertia_moment_2d_algo.rotation_center_x = 1024
inertia_moment_2d_algo.rotation_center_y = 1024
inertia_moment_2d_algo.rotation_angle = 10
inertia_moment_2d_algo.execute()

print( 
print("meanMoment: ", inertia_moment_2d_algo.output_measurement.mean_moment( 0 ) ) );

ImageView polystyrene_sep = Data.ReadVipImage( @"Data/images/polystyrene_sep.vip" );

InertiaMoment2d inertiaMoment2dAlgo = new InertiaMoment2d
{
    inputBinaryImage = polystyrene_sep,
    rotationCenterX = 1024,
    rotationCenterY = 1024,
    rotationAngle = 10
};
inertiaMoment2dAlgo.Execute();

Console.WriteLine( "meanMoment: " + inertiaMoment2dAlgo.outputMeasurement.meanMoment( 0 ) );

Function Examples

auto polystyrene_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene_sep.vip" );

auto result = inertiaMoment2d( polystyrene_sep, 1024, 1024, 10 );

std::cout << "meanMoment: " << result->meanMoment( 0 ) ;

polystyrene_sep = imagedev.read_vip_image(imagedev_data.get_image_path("polystyrene_sep.vip"))

result = imagedev.inertia_moment_2d( polystyrene_sep, 1024, 1024, 10 )

print( "meanMoment: ", result.mean_moment( 0 ) );

ImageView polystyrene_sep = Data.ReadVipImage( @"Data/images/polystyrene_sep.vip" );

MeanInertiaMomentMsr result = Processing.InertiaMoment2d( polystyrene_sep, 1024, 1024, 10 );

Console.WriteLine(  "meanMoment: " + result.meanMoment( 0 )  );

InertiaMoment2d

- Function Syntax

+ Class Syntax

Parameters

Object Examples

Function Examples

Function Syntax

Class Syntax